Prince Turki bin Nasser knows a thing or two about living well. When he needs to move his Rolls-Royce from Los Angeles to Dhahran, apparently he hires a plane to do it, at a cost of £165,000. When he wants to take his family on holiday, he has a retinue of servants, drivers and bodyguards.

In Paris, the prince is said to stay at the George V; in Beverly Hills he favours the Hilton. In London, it seems, he slums it in the Carlton Tower's presidential suite for £1,100 a night. He travels a lot.

It's the kind of lifestyle that few ordinary people have experienced. And it will surprise many to hear that BAE Systems, a major supplier of warplanes, missiles and warships to the UK, appears to have footed many of the Saudi prince's bills.

That, at least, is what company documents now being examined by the Serious Fraud Office seem to say. Prince Turki was an arms-procurement official for the Saudi government, and SFO investigators are trying to find out whether BAE's alleged acts of generosity towards him and others amounted to bribes, handed over in exchange for lucrative orders and concealed by false accounting.

Last week, the SFO raided several homes and arrested Wing Commander Tony Winship, a former BAE customer-relations executive who has been accused in the media of helping to organise alleged payments. Winship and another man were questioned before being released without charge. Two travel firms allegedly used as conduits for payments are also involved in the inquiry.

BAE, whose shares have wobbled since news of the raids broke, says it has not broken any laws. The company has also suggested that it is not itself the target of the SFO investigation; indeed, it is 'possible that BAE may itself have been the victim of fraud'. Still, BAE has a problem. Thanks to the investigative efforts of the Guardian, The Observer 's sister newspaper, much of what the SFO may be probing has already reached the public domain - and, unless quickly disproved, it is supremely embarrassing for Britain's leading defence firm.

Internal documents and the testimony of 'whistleblowers' have been gathered by the Guardian over the past year. These suggest that between 1990 and 2002 the company ran a 'slush fund' that showered £60m worth of secret payments and gifts on selected Saudis, including top-of-the-range cars, luxury holidays and other VIP services.

A civil servant at the Ministry of Defence, who also allegedly benefited from BAE's largesse, was arrested and interviewed before being released without charge in September.

Sir Dick Evans, BAE's recently retired chairman, has publicly denied in the past that the company paid bribes and is now facing pressure to explain the alleged Saudi payments. Steven Mogford, the company's chief operating officer, may also be required to deal with claims that, according to documents, he personally authorised some payments to Saudis.

For its part, BAE has explicity denied operating a slush fund or using false accounting to hide payments to Saudi officials and others. Beyond that, it has declined to discuss specific allegations in detail, saying it 'rigorously complies with the laws of the UK and of the countries in which it operates'.

Much may hinge on the timing of the alleged payments. In this country, it did not become a criminal offence to bribe foreign officials until 2002. Most of the transactions in question took place in the 1990s, so BAE might not have a case to answer even if they were 'payments for contracts'.

But pre-2002 laws existed against domestic corruption, and the SFO will want to know whether any such payments were made inside the UK. It will also want to check claims that one or two payments may have been made after the 2002 law came into force. And how BAE recorded the transfers is also of key importance, since at the moment the SFO is primarily concerned with possible false accounting.

BAE says it is unable to speak freely because of client confidentiality. But company sources have hinted the expenses in question were actually 'contract overheads passed on to the customer' - in other words, BAE was ultimately reimbursed for the lavish hotel and air travel bills by Saudi Arabia itself. Whether that would exonerate BAE remains to be seen.

Whatever the case, trouble like this doesn't help BAE market its services to would-be clients. The SFO inquiry could put pressure on the company's relationship with its most important customer, the British government. And then there is the question of what the Saudis will think of the ruckus.

Under the Al Yamamah agreement signed between Britain and Saudi Arabia in 1985, BAE has supplied an estimated £50 billion worth of military equipment to the kingdom. It is still one of the company's biggest clients.

The Saudi embassy in London emphasises that it 'does not condone corrupt practices of any kind'. Prince Turki has not yet commented. But at BAE's headquarters, they will be praying that Riyadh's publicity-shy princes and paymasters don't start looking for a new supplier and a quieter life.